Self-similarity and Lamperti transformation for random fields

Marc G. Genton*, Olivier Perrin, Murad S. Taqqu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We define multi-self-similar random fields, that is, random fields that are self-similar component-wise. We characterize them, relate them to stationary random fields using a Lamperti-type transformation and study these stationary fields. We also extend the notions of local stationarity and local stationarity reducibility to random fields. Our work is motivated by applications arising from climatological and environmental sciences. We illustrate these new concepts with the fractional Brownian sheet and the Lévy fractional Brownian random field.

Original languageEnglish (US)
Pages (from-to)397-411
Number of pages15
JournalStochastic Models
Issue number3
StatePublished - Jul 2007
Externally publishedYes


  • Fractional Brownian sheet
  • Lamperti transformation
  • Local stationarity
  • Lvy fractional Brownian random field
  • Random field
  • Reducibility
  • Self-similarity

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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